Two-stage-to-orbit (TSTO) hypersonic vehicle is considered one of the most promising next-generation reusable launch vehicle (RLV) systems for its efficiency and reliability, but the safe separation of two-body system determines the success of TSTO missions. Hypersonic flows around a TSTO-like two-body system are studied by CFD (computational fluid dynamics) dynamic simulations at Mach 7. The TSTO model, which consists of two three-dimensional (3-D) wedges as orbiter and booster, is used to investigate the interstage aerodynamic interferences and separation characteristics with different stage separation schemes. This paper analyzes in detail the transverse stage separation (TSS) scheme, where the orbiter moves along the direction normal to the upper surface of the booster. Besides, the longitudinal stage separation (LSS) scheme, in which the orbiter moves rapidly along the flight direction of the booster, is proposed. The numerical results of dynamic simulation show that the complex interstage aerodynamic interference is accompanied by the combined action, including the disturbance of wave/boundary-layer interaction, shock/wake-flow interaction, and a horseshoe vortex (or a “˄” vortex). Moreover, the flow characteristics and the physical mechanism of TSTO separation are clarified by analyzing the changes of flow structure and the topologies of 3-D separation flow. The intensity of the aerodynamic interference increases with increasing angle of incidence (AoI), but decreases with the increase of clearance during TSS. The ideal values of AoI for TSTO TSS are 6° and 8°. For LSS, the orbiter can safely separate from the booster at angle of attack (AoA) = 5° and 10° cases while the collision occurs at AoA = 0° case. The proper AoA value of the safe LSS is 5°. Since the interference load on the stages in LSS is smaller than that in TSS, the LSS is ideal for stage separation of TSTO.